Memory game: conditional probability

This task assesses how well students understand calculating conditional probability. Some of the tasks require either systematic listing or use of  tree diagrams.

The task features a ‘memory game’. In the game there are four cards, two have a picture of an apple on them, and two have a picture of bananas. In order to ‘win’ the player must turn over two cards that are the same. The initial task is to calculate the probability of winning when only one of the four cards is known.

After an initial unsuccessful turn, the cards are left in the same place. The task is again to work out the probability of winning.

The game is then changed by the addition of two cards with pictures of an orange. Students must calculate the probability of getting two cards the same. A final question asks: ‘what is the probability of getting two cards that show bananas.’

Students will need to have a firm understanding of conditional probability to be successful with these tasks.

This task is from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. A full rubric is given for the task, together with examples of student work and suggestions for helping students overcome misconceptions. Further information on the collection is given here.